Monday, January 17, 2011

Why Do People Gamble?

I was in Vegas last weekend, doing field research ;) on utility functions. People clearly like to gamble, and are willing to pay a premium for the exposure to random payoffs with large skew. This is contrary to the usual assumption that people are risk averse, and necessitate a positive expected return to take a gamble. Early on in utility theory, Friedman and Savage (1948) siezed on this anomaly to argue that the curvature of an individual's utility function differs based upon the amount of wealth the individual has. This curving utility function would thereby explain why an individual is risk-loving when he has less wealth (e.g., by playing the lottery) and risk-averse when he is wealthier (e.g., by buying insurance). Harry Markowitz, a former student of Friedman's, argued the implications of the Friedman–Savage utility function were paradoxical. Specifically, its implication that those at the highest level of income would never take risks. His solution was to relate the curvature of an individual's utility function to increases in wealth.

Thus, from the very begining, utility theory was problematic. Solutions had a whack-a-mole tendency to rid one anomaly and create another. The basic problem is that

1) People pay to buy insurance.2) People pay to gamble.

It's still a puzzle, though every so often a new paper shows up to solve it (eg, Kahneman and Tversky's prospect theory). I think people's paying for risky investments that are a function of skill makes total sense in a search for alpha, discovering one's comparative advantage. Yet, the pure randomness of much gambling--slots, roulette, craps--makes no sense unless you assume people have some belief in luck.

There may be a much simpler explanation. Have you considered gambling analogous to paying for entertainment? Perhaps people enjoy playing a few hours of blackjack (or any other casino game) and are will to pay to do it. Sure the outlier event is nice but most people aren't playing with enough money on the table such that even if they have a big win it will change their lives substantially (I suppose slots is excepted in this regard).

Maybe it is about being stupid - or at least about not knowing how to evaluate costs and benefits.

Really, insurance and the lottery are different ends of the same spectrum. The same person who buys too much insurance (reaping a net negative return) may also buy lottery tickets (reaping a net negative return). In each case, the person is paying a small sum in order to deal with an unlikely, but large, potentiality. The only difference is whether they're trying to shield themselves from that potentiality, or trying to expose themselves to it.

Gambling is excitement and fun. People pay for sex, they pay for gambling.

People does not play for money but for excitement. It is wrong to study it as an economic, profit-making activity. It appears that monstruously large prizes (with infinitesimal chances) cause the most excitement and people is willing to pay the most to play that game.

Actually, if you consider playing the lottery and buying insurance as the same thing (managing unlikely, but large, potentialities) then it's easy to explain why rich people buy insurance and don't play the lottery while poor people play the lottery and don't buy insurance.

Poor people are near to a floor below which they are not likely to sink, even if they incur some large liability. Bankruptcy, the social safety net, and the general consensus that you can't squeeze blood out of a turnip mean that the poor just don't face much downside from events that one might typically buy insurance against.

Rich people, on the other hand, face large downside risks, and so they buy a lot of insurance. At the same time, they face a smaller upside to winning the lottery than do poor people, because they're already rich. A few more million would be nice, but would certainly be less life-changing than it would be to someone living paycheck to paycheck.

So the rich protect against downside risk while the poor try to expose themselves to upside risk, so to speak.

One more thought. Regarding Markowitz and the idea that the wealthiest people would never take risks: I know a man who made millions as co-founder of a well-known time management company. He later lost millions trying to start an airline. My feeling is that he got a bit bored with life and wanted the excitement and work of a large project - and that desire caused him to be incautious with his new venture. I don't think this is such an uncommon story.

Upshot: an individual's utility function can be complicated and affected by many variables. Maybe level of wealth dominates the utility function when wealth is low, and maybe other variables dominate the utility function when a person's wealth exceeds some threshold.

I recently started to play the Lotto in my state (CA). I buy one ticket for a $1 about once per week or annually about $50. In the past I thought that the Lotto was a waste of money but I realized that the marginal value of a dollar (or fifty over a year) is virtually zero to me as I make a good living. I certainly spend more on coffee per month or food that I throw away, etc. The gain is the possibility of winning (remote as that is) plus the entertainment value of checking my numbers. I am not so rich that a jackpot would not significantly change my life. So I am wondering how the falling marginal value of a dollar as one's salary/wealth goes up plays into the decision to gamble and how it is taken into account?

Interestingly, I've shared this argument with some of my friends who are in similar situations and they either think I am stupid or have started to buy an occasional ticket themselves.

Gambling naturally appeals to the emotional and aesthetic parts of human nature and generally one needs to work very hard to think (unnaturally)in close to pure mathematical terms to either avoid gambling altogether or try and develop a winning strategy.

General intelligence doesn't make as big a difference in terms of inclination to gamble as some claim. Having at one time worked in high-end retail brokerage I can tell you that there are plenty of smart, successful Asian men that love to gamble (in securities markets anyway). Heck, even Einstein liked to go to Vegas and play cards. "Al from Jersey" as his friends would introduce him.

People gamble because they implicitly want something for nothing, and are willing to lose to pursue it. It stems from a hatred of God, who commands work, and that recreation be legitimate, without taint. People like taint.

Pat...that's probably true, but the big problem is then that investments with large negative skew should have higher returns, and we don't see that (eg, junk bonds). So, I see your explanation working for small sums, but it doesn't generalize well. I think the nature of the risk--one chance outside our ken, one chance influenced by our 'luck'.

Eric, If there are negatively skewed assets without large expected returns, then I'd think many people would regard them as bad investments. But I don't see how that impacts on what I was saying.

The issue is that if I buy both insurance and lottery tickets, that is regarded as bizarre behavior by some. I'm just saying that I see that as consistent with a reasonable utility function, and I don't really understand why some think it bizarre.

I'm guessing that the issue is that one behavior is classified as risk-averse and the other as risk-seeking.